f(x) = Σ_n=0∞ (f⁽ⁿ⁾(a)/n!)(x-a)ⁿ sin 2θ = 2 sinθ cosθ (x-h)² + (y-k)² = r² d/dx(cos x) = -sin x αβ = c/a ε = -dΦ/dt ln(P₂/P₁) = -ΔH_vap/R (1/T₂ - 1/T₁) P_solution = X_solvent × P^°_solvent c = λf v² = u² + 2as log_b a = ln a/ln b a_n = a + (n - 1)d m = f'(x) T = 2π√(L/g) V = L(dI/dt) d/dx(ln x) = 1/x d/dx(sin x) = cos x (a+b)ⁿ = Σ_k=0ⁿ (nCk)a^n-kb^k y - y₁ = m(x - x₁) E = VIt Equivalent Weight = Molecular Weight/n sin x = Σ (-1)ⁿ x⁽²ⁿ⁺¹⁾/(2n+1)! x = a sinθ cos x = Σ (-1)ⁿ x⁽²ⁿ⁾/(2n)! F = ma

A = Pe^rt d/dx(e^x) = e^x (1+x)ⁿ = Σ ⁿ C _k.x^k e^x = Σ xⁿ/n! pH = -log[H⁺] F_c = mv²/r λ = h/p F = k( q₁q₂ )/r² lim_x→a f(x)/g(x) = lim_x→a f'(x)/g'(x) E = E° - (0.0591/n) log Q Φ = BA cosθ s = (a+b+c)/2, A = √(s(s-a)(s-b)(s-c)) F = q(E + v × B) n = c/v cos 2θ = cos²θ - sin²θ d = √((x₂-x₁)²+(y₂-y₁)²) (f(g(x)))' = f'(g(x))⋅g'(x) C(n, r) = n!/(r!(n-r)!) F_x + F_y(dy/dx) = 0 1/f = 1/v + 1/u (Σ a_i²)(Σ b_i²) ≥ (Σ a_ib_i)² W = Fd cosθ U = mgh sin²(θ/2) = (1 - cosθ)/2 S = a/(1 - r)

a_n = ar^{n - 1} A = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)| A = πab V = IR Percent Purity = (mass of pure substance/mass of sample) × 100 f'(a) = lim_h→0 (f(a+h)-f(a))/h ∫ u dv = uv - ∫ v du n₁ sinθ₁ = n₂ sinθ₂ Rate = k[A]^m[B]ⁿ pK_a = -log K_a K.E. = ½mv² x = [-b ± √(b² - 4ac)]/(2a) π = MRT a_c = v²/r cos²(θ/2) = (1 + cosθ)/2 A = ab sinθ ΔG = ΔH - TΔS p = mv A = ∫_a^b f(x) dx P(n, r) = n!/(n-r)! A = ½ab sin C Q = It e = (v₂ - v₁)/(u₁ - u₂) E = hf P = IV

Normality = Molarity × n S_n = (n/2)[2a + (n - 1)d] s = ut + ½at² sin A + sin B = 2 sin((A+B)/2) cos((A-B)/2) m = (y₂ - y₁)/(x₂ - x₁) f(x) = Σ_n=0∞ (f⁽ⁿ⁾(0)/n!)xⁿ α + β = -b/a f''(x) ΔT_b = iK_bm I = ½ Σ c_i z_i² V = (4/3)πr³ K_c = ([C]^c[D]^d)/([A]^a[B]^b) d = |Ax₀ + By₀ + C|/√(A²+B²) P = W/t 2 sin A cos B = sin(A+B) + sin(A-B) v = u + at sin²θ + cos²θ = 1 M = moles/volume n = mass/M ∫(dx/x) = ln|x| + C S_n = a(1 - rⁿ)/(1 - r) ΔT_f = iK_fm